Impact of a block structure on the Lotka-Volterra model - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Impact of a block structure on the Lotka-Volterra model

Résumé

The Lotka-Volterra (LV) model is a simple, robust, and versatile model used to describe large interacting systems such as food webs or microbiomes. The model consists of n coupled differential equations linking the abundances of n different species. We consider a large random interaction matrix with independent entries and a block variance profile. The ith diagonal block represents the intra-community interaction in community i, while the off-diagonal blocks represent the inter-community interactions. The variance remains constant within each block, but may vary across blocks. We investigate the important case of two communities of interacting species, study how interactions affect their respective equilibrium. We also describe equilibrium with feasibility (i.e., whether there exists an equilibrium with all species at non-zero abundances) and the existence of an attrition phenomenon (some species may vanish) within each community. Information about the general case of b communities (b > 2) is provided in the appendix.
Fichier principal
Vignette du fichier
Article_Bloc_v0.pdf (1.47 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04298668 , version 1 (21-11-2023)

Identifiants

Citer

Maxime Clenet, François Massol, Jamal Najim. Impact of a block structure on the Lotka-Volterra model. 2023. ⟨hal-04298668⟩
28 Consultations
13 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More